Question

Find the inverse, converse and contrapositive of the statement: "it is not raining is a sufficient condition for my visit to town."

a) inverse: It is raining is a necessary condition for my visit to town.
converse: My visit to town is a sufficient condition for it not raining.
contrapositive: My visit to town is a necessary condition for it raining.
b) inverse: It is raining is not a necessary condition for my visit to town.
converse: My visit to town is a necessary condition for it raining.
contrapositive: My visit to town is not a sufficient condition for it raining.
c) inverse: It is not raining is not a sufficient condition for my visit to town.
converse: My visit to town is a necessary condition for it not raining.
contrapositive: My visit to town is a sufficient condition for it raining.
d) inverse: It is raining is a sufficient condition for my visit to town.
converse: My visit to town is not a necessary condition for it raining.
contrapositive: My visit to town is not a sufficient condition for it not raining.

Answer 1

The inverse, converse, and contrapositive of the statement 'It is not raining is a sufficient condition for my visit to town' are as follows: inverse - 'It is raining is a necessary condition for my visit to town', converse - 'My visit to town is a sufficient condition for it not raining', and contrapositive - 'My visit to town is a necessary condition for it raining'.

Step-by-step explanation:

Inverse:

Statement: It is not raining is a sufficient condition for my visit to town.

Inverse: It is raining is a necessary condition for my visit to town.

Converse:

Statement: It is not raining is a sufficient condition for my visit to town.

Converse: My visit to town is a sufficient condition for it not raining.

Contrapositive:

Statement: It is not raining is a sufficient condition for my visit to town.

Contrapositive: My visit to town is a necessary condition for it raining.